1. Warm Up Change each percent to a decimal. 1. 73% 2. 112% 3. 0.6% 4. 1%
1. 73% %
3. 0.6% %
Change each fraction or mixed number to a decimal.
Solve each proportion.
0.73
1.12
0.006
0.01
0.5
0.3
0.8
1.2 12
4.2

2. A percent is a ratio that compares a number to 100. For example,
To find the fraction equivalent of a percent write the percent as a ratio with a denominator of 100. Then simplify.
25% = 25
100 = 1 4
To find the decimal equivalent of a percent, divide by 100.
25% = 25
100
= 0.25

3. Some Common Equivalents
Percent
Fraction
Decimal
100%
40%
25%
20%
50%
60%
75%
80%
10%

4. Some Common Equivalents
Percent
Fraction
Decimal
100%
40%
25%
20%
50%
60%
75%
80%
10%
The greatest percent shown in the table is 100% or 1. But percents can be greater than 100%. For example, 120% = = 1.2. You can also find percents that are less than 1%. For example, 0.5%= = You can use the proportion = to find unknown values.

5. Example 1: Finding the Part
Find 30% of 80.
Method: Use an equation.
x = 30% of 80
Write an equation. Let x represent the part.
x = .3(80)
Write the percent as a decimal and multiply.
x = 24
30% of 80 is 24.
Check 30% is the same as , and of 80 is 24. 

6. Example 2: Finding the Part
Find 120% of 15.
Method: Use an equation.
x = 120% of 15
Write an equation. Let x represent the part.
x = 1.20(15)
Write the percent as a decimal and multiply.
x = 18
120% of 15 is 18.

7. Check It Out! Example 1b
Find 20% of 60.
Method: Use an equation.
x = 20% of 60
Write an equation. Let x represent the part.
x = .2(60)
Write the percent as a decimal and multiply.
x = 12
20% of 60 is 12.

8. Check It Out! Example 1b
Find 210% of 8.
Method: Use an equation.
x = 210% of 8
Write an equation. Let x represent the part.
x = 2.10(8)
Write the percent as a decimal and multiply.
x = 17
210% of 8 is 16.8.

9. Check It Out! Example 1c
Find 4% of 36.
Method 2 Use an equation.
x = 4% of 36
Write an equation. Let x represent the part.
x = .04(36)
Write the percent as a decimal and multiply.
x =1.44
4% of 36 is 1.44.

10. Example 2A: Finding the Percent
What percent of 45 is 35? Round your answer to the nearest tenth.
Method 1 Use a proportion.
Use the percent proportion.
Let x represent the percent.
45x = 3500
Find the cross products.
Since x is multiplied by 45, divide both sides by 45 to undo the multiplication.
x ≈ 77.8
35 is about 77.8% of 45.

11. Example 2B: Finding the Percent
230 is what percent of 200?
Method: Use a equation.
230 = x • 200
Write an equation. Let x represent the percent.
230 = 200x
Since x is multiplied by 200, divide both sides by 200 to undo the multiplication.
1.15 = x
The answer is a decimal.
115% = x
Write the decimal as a percent. This answer is reasonable; 230 is more than 100% of 200.
230 is 115% of 200.

12. Check It Out! Example 2a
What percent of 35 is 7?.
Method 1 Use a proportion.
Use the percent proportion.
Let x represent the percent.
35x = 700
Find the cross products.
Since x is multiplied by 35, divide both sides by 35 to undo the multiplication.
x = 20
7 is 20% of 35.

13. Check It Out! Example 2b
27 is what percent of 9?
Method 2 Use an equation.
27 = x • 9
Write an equation. Let x represent the percent.
27 = 9x
Since x is multiplied by 9, divide both sides by 9 to undo the multiplication.
The answer is a whole number.
3 = x
300% = x
Write the whole number as a percent. This answer is reasonable; 27 is more than100% of 9.
27 is 300% of 9.

14. Example 3A: Finding the Whole
38% of what number is 85? Round your answer to the nearest tenth.
Method 1 Use a proportion.
Use the percent proportion.
Let x represent the whole.
38x = 8500
Find the cross products.
Since x is multiplied by 38, divide both sides by 38 to undo the multiplication.
x = 223.7
38% of about is 85.

15. Example 3B: Finding the Whole
20 is 0.4% of what number?
Method 2 Use an equation.
Write an equation. Let x represent the whole.
20 = 0.4% of x
20 = • x
Write the percent as a decimal.
Since x is multiplied by 0.004, divide both sides by to undo the multiplication.
5000 = x
20 is 0.4% of 5000.

16. Check It Out! Example 3a
120% of what number is 90?
Method 1 Use a proportion.
Use the percent proportion.
Let x represent the whole.
120x = 9000
Find the cross products.
Since x is multiplied by 120, divide both sides by 120 to undo the multiplication.
x = 75
120% of 75 is 90.

17. Check It Out! Example 3b
48 is 15% of what number?
Method 2 Use an equation.
Write an equation. Let x represent the whole.
48 = 15% of x
48 = 0.15 • x
Write the percent as a decimal.
Since x is multiplied by 0.15, divide both sides by 0.15 to undo the multiplication.
320 = x
48 is 0.15% of 320.

18. Example 4: Application
The serving size of a popular orange drink is 12 oz. The drink is advertised as containing 5% orange juice. How many ounces of orange juice are in one serving size?
Use the percent proportion.
Let x represent the percent.
100x = 60
Since x is multiplied by 100, divide both sides by 100 to undo the multiplication.
x = 0.6
A 12 oz orange drink contains 0.6 oz of orange juice.

19. Check It Out! Example 4
Use the information above to find the number of karats in a bracelet that is 42% gold. Round your answer to the nearest whole number.
Use the percent proportion.
Let x represent the number of karats.
100x = 1008
Since x is multiplied by 100, divide both sides by 100 to undo the multiplication.
x = 10.08
A ring that contains 42% gold is about 10 karats.

20. Lesson Quiz: Part 1
Find each value. Round to the nearest tenth if necessary.
1. Find 20% of 80.
2. What percent of 160 is 20?
3. 35% of what number is 40?
is what percent of 80?
5. Find 320% of 8.
6. 65 is 0.5% of what number? 16
12.5%
114.3
150%
25.6
13,000

21. Lesson Quiz: Part 2
Find each value. Round to the nearest tenth if necessary.
7. A survey at a local school showed that 38% of the students chose chocolate ice cream as their favorite ice cream. Eight hundred students took the survey. How many chose chocolate ice cream?
304